2017/05/16 by Randall L. Rathbun, Rathbun, Randall L.
Mathematics · Physics and Astronomy · #Mathematics and Applications #Advanced Mathematical Theories and Applications
paper · pdf · doi:10.48550/arxiv.1705.05929
Integer cuboids are rectangular Diophantine parallelepipeds It has been discovered that these cuboids come in 3 varieties: Euler or body type, edge type, and face type. In all three cases, one edge or diagonal is irrational, all six others are rational. We discuss an exhaustive computer search procedure which uses the Pythagorean group Py(n) to locate all possible cuboids with a given edge n. Over the range of 44 to 200,000,000,027 for the smallest edge, 167,043 cuboids were discovered. They are listed in the Integer Cuboid Table.